Question

Can anyone help me with the derivative of:
y=x^11 e^x

Answer 1

\[y=x ^{11}e ^{x}\] Much easier to look at.

Answer 2

do you know the product rule

Answer 3

Yeah, I somehow worked out the problem by myself. Just want to make sure if I got it right or not.

Answer 4

well tell me what you got :)

Answer 5

I look really ridiculous, but: \[11x ^{10}e ^{x}+x ^{11}e ^{x}\] Here you go.

Answer 6

looks right to me

Answer 7

hm....ok, if you say so. I just don't feel right somehow. It look too long and weird.

Answer 8

It's right!
\(u=x^{11} => u' = 11x^{10}\)
\(v=e^{x} => v' = e^{x}\)
\(=> 11x^{10}*e^{x}+ x^{11}e^{x}\)

Answer 9

You can also write it like: \(e^{x} (11x^{10}+x^{11})\)
if it looks too "weird" :)

Answer 10

ok, thanks :D

Answer 11

You could also factor the \[x ^{10}\]and express the derivative as\[\frac{ dy }{ dx }=x ^{10}e ^{x}(11+x)\]

Answer 12

Cool, thanks